AP State Syllabus AP Board 8th Class Maths Solutions Chapter 6 Square Roots and Cube Roots Ex 6.1 Textbook Questions and Answers.

## AP State Syllabus 8th Class Maths Solutions 6th Lesson Square Roots and Cube Roots Exercise 6.1

Question 1.

What will be the units digit of the square of the following numbers?

(i) 39

(ii) 297

(iii) 5125

(iv) 7286

(v) 8742

Solution:

Number | Square of the units digIt | Units digit of a squared number |

i) 39 | 9^{2} = 9 x 9 = 81 |
1 |

ii) 297 | 7^{2} = 7 x 7 = 49 |
9 |

Iii) 5125 | 5^{2} = 5 x 5 = 25 |
5 |

iv) 7286 | 6^{2} = 6 x 6 = 36 |
6 |

v) 8742 | 2^{2} = 2 x 2 = 4 |
4 |

Question 2.

Which of the following numbers are perfect squares?

(i) 121

(ii) 136

(iii) 256

(iv) 321

(v) 600

Solution:

Number | Prime factorizatlon | Perfect square numbers Yes/No |

i) 121 | 121 = 11 x 11 = 11^{2} |
yes |

ii) 136 | 136 = 8 x 17 = 2 x 2 x 2 x 17 | No |

iii) 256 | 256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 2^{8 }= (2^{4})^{2} |
yes |

iv) 321 | 321 = 3 x 107 | No |

v) 600 | 600 = 120 x 5 = 12 x 10 x 5 = 2 x 2 x 2 x 3 x 5 x 5 | No |

Question 3.

The following numbers are not perfect squares. Give reasons?

(i) 257

(ii) 4592

(iii) 2433

(iv) 5050

(v) 6098

Solution:

i) 257 → The units digit of the number is 7. So it is not a perfect square number.

ii) 4592 → The units digit of the number is 2. So it is not a perfect square number.

iii) 2433 → The units digit of the number is 3. So, it is not a perfect square number.

Iv) 5050 → The last two digits of the number are not two zero’s. So, it is not a perfect square number.

v) 6098 → The units digit of the number is 8. So It is not a perfect square number

Question 4.

Find whether the square of the following numbers are even or odd?

(i) 431

(ii) 2826

(iii) 8204

(iv) 17779

(v) 99998

Solution:

Number | Units digit of square of a number | Even / Odd |

(i) 431 | 1^{2} = 1 |
1 , odd |

(ii) 2826 | 6^{2 }= 36 |
6, odd |

(iii) 8204 | 4^{2} = 16 |
6 , even |

(iv)17779 | 9^{2 }= 81 |
1 , odd |

(v) 99998 | 8^{2 }= 64 |
4 , even |

Question 5.

How many numbers lie between the square of the following numbers

(i) 25; 26

(ii) 56; 57

(iii) 107;108

Solution:

The numbers lie between the square of the numbers are:

1) 25,26 → 2 x 25=50

ii) 56, 57 → 2 x 56 = 112

iii) 107, 108 → 2 x 107 = 214

Question 6.

Without adding, find the sum of the following numbers

(i) 1 + 3 + 5 + 7 + 9 =

(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 =

(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 =

Solution:

(i) 1 + 3 + 5 + 7 + 9 = (5)^{2} = 5 x 5 = 25

[∵ Sum of ‘n’ consecutive odd number = n^{2}]

(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 9^{2} = 9 x 9 = 81

(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 = 13^{2} = 13 x 13 = 169